Light field integration in SUGRA theories

TL;DR

This paper analyzes the conditions under which integrating out certain fields in N=1 Supergravity yields a reliable two-derivative effective theory, especially when fields have masses near the supersymmetry breaking scale.

Contribution

It provides a supersymmetric framework for integrating out fields with comparable masses to the SUSY breaking scale, ensuring the validity of the two-derivative description under specific conditions.

Findings

Two-derivative description is reliable when equations of motion are stable and analytically continued F-flatness conditions are valid.

Nearly decoupled models with two chiral sectors can be consistently integrated out.

Gauge symmetries can be incorporated if they are factorized between hidden and visible sectors.

Abstract

We revisit the integration of fields in N=1 Supergravity with the requirement that the effective theory has a reliable two-derivative supersymmetric description. In particular we study, in a supersymmetric manifest way, the situation where the fields that are mapped out have masses comparable to the Supersymmetry breaking scale and masses of the remaining fields. We find that as long as one stands in regions of the field configuration space where the analytic continuation to superspace of the F-flatness conditions be reliable equations of motion for the fields that are being mapped out, and provided their solutions are stable regardless the dynamics of the remaining fields, such a two-derivative description is a reliable truncation of the full effective theory. The study is mainly focused to models with two chiral sectors, H and L, described by a Kaehler invariant function with schematic dependencies of the form G=G_H(H,\bar H)+G_L(L,\bar L), which leads to a nearly decoupled theory that allows the previous requirements to be easily satisfied in a consistent way. Interestingly enough for the matters of our study this kind of models present an scenario that is as safe as the one presented in sequestered models. It is also possible to allow gauge symmetries as long as these appear also factorized in hidden and visible sectors. Then, the integration of the hidden vector superfields is compulsory and proceeds reliably through the D-flatness condition analytically continued to superspace.